DOI QR코드

DOI QR Code

COMMON FIXED POINTS FOR TWO MAPPINGS WITH EXPANSIVE PROPERTIES ON COMPLEX VALUED METRIC SPACES

  • 투고 : 2013.10.29
  • 심사 : 2015.01.27
  • 발행 : 2015.02.15

초록

In this paper, we use two mappings satisfying certain expansive conditions to construct convergent sequences in complex valued metric spaces, and then we prove that the limits of the convergent sequences are the points of coincidence or common fixed points for the two mappings. The main theorems in this paper are the generalizations and improvements of the corresponding results in real metric spaces, cone metric spaces and topological vector space-valued cone metric spaces.

키워드

참고문헌

  1. A. Azam, B. Fisher, and M. Khan, Common fixed point theroems in complex valued metric spaces, Numer Funt Anal Optim. 32 (2011), no. 3, 243-353. https://doi.org/10.1080/01630563.2011.533046
  2. C. D. Bari and P. Vetro, ${\phi}$-pairs and common fixed points in cone metric spaces, Rendiconti del circlol Mathematico. 57 (2008), 279-285.
  3. I. Beg, A. Azam, and M. Arshad, Common fixed points for mapps on Topological vector space valued cone metric spaces, Inter. J. Math. and Math. Sci. 2009, doi:10.1155, ID 560264.
  4. A. S. Cvetkovic, M. P. Stanic, S. Dimitrijevic, and S. Simic, Common fixed point theorems for four mappings on cone metric type spaces, Fixed Point Theory and Applications, 2011, Aeticle ID 589725, doi:10.1155/2011/589725.
  5. S. N. He, Fixed point theorems on II, III expansive mappings, Journal of Civil Aviation University of China(Chinese Series) 22 (2004), no. 5, 50-52.
  6. S. N. He, A fixed point theorem on the weak expansive mapping, Journal of Nanjing University Mathematical Biquarterly(Chinese Series) 23 (2006), no. 2, 334-340.
  7. L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  8. Z. Kadelburg, P. P. Murthy, and S. Radenovic, Common fixed points for expansive mappings in cone metric spaces, Int. Journal of Math. Analysis 27 (2011), no. 5, 1309-1319.
  9. Y. J. Piao, Fixed point theorems for III,s-III-expansive mappings on CMTS, Journal of Systems Science and Mathematics Sciences(Chinese Series) 33 (2013), no. 8, 976-984.
  10. Y. J. Piao and Y. F. Jin, New unique common fixed point results for four mappings with ${\Phi}$-contractive type in 2-metric spaces, Applied Mathematics 7 (2012), no. 3, 734-737.
  11. F. Rouzkard and M. Imdad, Some common fixed point theroems on complex valued metric spaces, Computers and Mathematics with Applications 64 (2012), 1866-1874. https://doi.org/10.1016/j.camwa.2012.02.063
  12. I. Sahin and M. Telci, A theorem on common fixed points of expansion type mappings in cone metric spaces, An. St. Univ. Ovidius Constanta 18 (2010), no. 1, 329-336.
  13. W. Shatanawi and F. Awawdeh, Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed point theory and Applications, 2012, doi:10.1186/1687-1812-2012-19.
  14. W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and application, J. of Inequalities and Applications 84 (2012), 12pages.
  15. K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric space, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2012-189.
  16. M. P Stanic, A. S. Cvetkovic, S. Simic, and S. Dimitrijevic, Common fixed point under contractive condition of ciric's type on cone metric type spaces, Fixed Point Theory and Applications, 2012, doi:10.1186/1687-1812-2012-35.
  17. S. Z. Wang, B. Y. Li, and Z. M. Gao, Expansive mappings and fixed point theorems, Advances in Mathematics(Chinese Series) 11 (1982), no. 2, 149-153.

피인용 문헌

  1. COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS WITH ψ-ϕ-CONTRACTIVE OR EXPANSIVE TYPE CONDITIONS ON COMPLEX-VALUED METRIC SPACES vol.28, pp.3, 2015, https://doi.org/10.14403/jcms.2015.28.3.451